Finite Group Databasebeta

← #11872330

Subgroups — #11872330

Order 1152.

852 conjugacy classes of subgroups.

The subgroup lattice has 774 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595394C211yesmaximal, characteristic, complemented
2#10595217C211yesmaximal, characteristic, complemented
3#10592863C211yesmaximal, characteristic, complemented
4C3×#5172C211yesmaximal, characteristic, complemented
5C3×#5163C211yesmaximal, characteristic, complemented
6#10591586C211yesmaximal, characteristic, complemented
7#10591571C211yesmaximal, characteristic, complemented
8#10591547C211yesmaximal, characteristic, complemented
9#10591435C211yesmaximal, characteristic, complemented
10#10591428C211yesmaximal, characteristic, complemented
11#10591415C211yesmaximal, characteristic, complemented
12#10590767C211yesmaximal, characteristic, complemented
13#10590741C211yesmaximal, characteristic, complemented
14#10590699C211yesmaximal, characteristic, complemented
15#10590680C211yesmaximal, characteristic, complemented
16#80364—31nomaximal
17#80072—31nomaximal
18C2×C3×#239C2211yescharacteristic
19C2×C32×SD16C2211yescharacteristic
20Q8×C3⋊Dic3C2211yescharacteristic
21D4×C3⋊Dic3C2211yescharacteristic
22C3×Q8×Dic3C2211yescharacteristic
23C2×C3×#215C2211yescharacteristic
24C3×#940C2211yescharacteristic
25C3×#938C2211yescharacteristic
26C2×C3×#213C2211yescharacteristic
27#63980—21no—
28#63970—21no—
29#63969—21no—
30#63962—21no—
31#63908C2211yescharacteristic
32#63898—21no—
33#63898C2211yescharacteristic
34#63898C2211yescharacteristic
35Dic3×D12—21no—
36Dic3×D12C2211yescharacteristic
37D3×C4⋊Dic3—21no—
38D3×C4⋊Dic3C2211yescharacteristic
39#63869C2211yescharacteristic
40#63855—21no—
41#63855C2211yescharacteristic
42C2×#3713C2211yescharacteristic
43#63662C2211yescharacteristic
44#63659C2211yescharacteristic
45#63645C2211yescharacteristic
46#63642C2211yescharacteristic
47C3×#835C2211yescharacteristic
48C3×#832C2211yescharacteristic
49C3×#821C2211yescharacteristic
50C3×#821C2211yescharacteristic
51C3×(C2×D3)⋊C8C2211yescharacteristic
52C3×Dic3⋊C8C2211yescharacteristic
53#63575C2211yescharacteristic
54#63574C2211yescharacteristic
55#63573C2211yescharacteristic
56Dic3⋊(C3⋊C8)C2211yescharacteristic
57#63563C2211yescharacteristic
58#63563C2211yescharacteristic
59(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
60#63553C2211yescharacteristic
61#5827—31no—
62#5719—31no—
63#5619—31no—
64#5574—31no—
65C3×#460—31no—
66C3×#449—31no—
67#5238—31no—
68#5172—31no—
69#5172D311yescharacteristic, complemented
70#5164—31no—
71#5164—31no—
72#5164—61no—
73#5163D311yescharacteristic, complemented
74Dic3×SD16—31no—
75#5150—31no—
76Dic3×D8—31no—
77#5072—31no—
78#5034—31no—
79#5022—31no—
80#4847—31no—
81#4840—31no—
82#4796—31no—
83#4788—31no—
84#4785—31no—
85#4785—31no—
86#4777—31no—
87#4774—31no—
88#4766—31no—
89#4756—31no—
90#4736—31no—
91#4720—31no—
92C2×C32×Q8C2311yescharacteristic
93C2×C32×D4C2311yescharacteristic
94C22×C3⋊Dic3—21no—
95C2×C3×#67—21no—
96C2×C3×#67—21no—
97C2×C3×#67—21no—
98C3×#239—22no—
99C3×#239—22no—
100C2×C3×D12—21no—
101C2×C3×D12C2311yescharacteristic
102C2×C3×D12C2311yescharacteristic
103C2×C3×C4×D3—21no—
104C2×C3×C4×D3C2311yescharacteristic
105C2×#625—21no—
106C2×D3×Dic3—21no—
107C2×D3×Dic3—21no—
108C2×D3×Dic3—21no—
109C2×D3×Dic3—21no—
110C32×SD16—22no—
111C2×C32×C8C2311yescharacteristic
112#3757—21no—
113C4⋊(C3⋊Dic3)—21no—
114C4⋊(C3⋊Dic3)C2311yescharacteristic
115C4⋊(C3⋊Dic3)C2311yescharacteristic
116C4×C3⋊Dic3—21no—
117C4×C3⋊Dic3C2311yescharacteristic
118C2×C3⋊(C3⋊C8)C2311yescharacteristic
119C3×#217—21no—
120C3×#215—22no—
121C3×#213—22no—
122C3×C4⋊Dic3—21no—
123C3×C4⋊Dic3C2311yescharacteristic
124C3×C4⋊Dic3C2311yescharacteristic
125C3×C4×Dic3—21no—
126C3×C4×Dic3C2311yescharacteristic
127C2×C3×C3⋊C8C2311yescharacteristic
128C2×C3×C3⋊C8C2311yescharacteristic
129#3724—21no—
130Dic3⋊Dic3—21no—
131Dic3⋊Dic3—21no—
132Dic3⋊Dic3D411yescharacteristic
133Dic3⋊Dic3D411yescharacteristic
134(C2×D3)⋊Dic3—21no—
135(C2×D3)⋊Dic3—21no—
136(C2×D3)⋊Dic3—21no—
137(C2×D3)⋊Dic3—21no—
138(C2×D3)⋊Dic3D411yescharacteristic
139(C2×D3)⋊Dic3D411yescharacteristic
140#3713—22no—
141#3119—91noSylow
142C2×C3×#41—31no—
143C2×#239C2×D311yescharacteristic
144C2×C3×SD16—21no—
145C2×C3×SD16—31no—
146C2×C3×SD16C2×D311yescharacteristic
147C2×C3×SD16C2×D311yescharacteristic
148C2×C3×D8—31no—
149C3×#127—31no—
150C3×#121—31no—
151C3×C4×Q8—31no—
152Q8×Dic3—31no—
153Q8×Dic3—31no—
154Q8×Dic3—61no—
155Q8×Dic3C2×D311yescharacteristic
156C2×#215C2×D311yescharacteristic
157#940C2×D311yescharacteristic
158#939—61no—
159#939—61no—
160#939—61no—
161#938—31no—
162#938—61no—
163#938C2×D311yescharacteristic
164#935—61no—
165#935—61no—
166D4×Dic3—31no—
167D4×Dic3—31no—
168D4×Dic3—31no—
169D4×Dic3—31no—
170D4×Dic3—31no—
171D4×Dic3—61no—
172D4×Dic3—61no—
173D4×Dic3—61no—
174C2×#213—31no—
175C2×#213—31no—
176C2×#213C2×D311yescharacteristic
177#930—31no—
178#926—31no—
179#926—61no—
180C2×C4⋊Dic3—31no—
181C2×C4⋊Dic3—61no—
182#893—31no—
183#893—31no—
184#893—61no—
185D3×C4⋊C4—31no—
186D3×C4⋊C4—61no—
187#890—31no—
188#886—61no—
189#883—61no—
190C4×D12—31no—
191C4×D12—61no—
192#872—31no—
193#872—61no—
194#870—31no—
195C3×C4⋊C8—31no—
196C3×#103—31no—
197C3×#102—31no—
198C3×#102—31no—
199C3×#102—31no—
200C3×C22⋊C8—31no—
201#835—31no—
202#835—31no—
203#835—61no—
204#835C2×D311yescharacteristic
205#832—31no—
206#832—31no—
207#832—31no—
208#832—31no—
209#832—61no—
210#832C2×D311yescharacteristic
211#830—31no—
212#821—31no—
213#821—31no—
214#821C2×D311yescharacteristic
215#821C2×D311yescharacteristic
216(C2×D3)⋊C8—31no—
217(C2×D3)⋊C8C2×D311yescharacteristic
218#818—31no—
219#818—31no—
220#818—31no—
221#818—61no—
222#817—31no—
223#815—31no—
224#815—31no—
225#815—61no—
226Dic3⋊C8—31no—
227Dic3⋊C8C2×D311yescharacteristic
228C8×Dic3—31no—
229C8×Dic3—31no—
230#808—31no—
231#808—31no—
232#808—31no—
233#807—31no—
234C4⋊(C3⋊C8)—31no—
235C23×C32—21no—
236C22×C3×D3—21no—
237C22×C3×D3—21no—
238C22×C3×D3C2×D411yescharacteristic
239C32×Q8—21no—
240C32×Q8#4112yes—
241C32×D4—21no—
242C32×D4—21no—
243C2×C32×C4—21no—
244C2×C32×C4C2411yescharacteristic
245C2×C3⋊Dic3—21no—
246C2×C3⋊Dic3—21no—
247C2×C3⋊Dic3—81no—
248C2×C3⋊Dic3C2×D411yescharacteristic
249C2×C3⋊Dic3C2×D411yescharacteristic
250C3×#67—81no—
251C3×#67—81no—
252C3×#67—81no—
253C2×C3×Dic3—21no—
254C2×C3×Dic3—21no—
255C2×C3×Dic3C2×D411yescharacteristic
256C2×C3×Dic3C2×D411yescharacteristic
257C2×C3×Dic3C2×D411yescharacteristic
258C3×D12—24no—
259C3×D12—21no—
260C3×D12—21no—
261C3×D12—21no—
262C3×D12#4112yes—
263C3×C4×D3—24no—
264C3×C4×D3—21no—
265C3×C4×D3—21no—
266#625—81no—
267D3×Dic3—81no—
268D3×Dic3—81no—
269D3×Dic3—81no—
270D3×Dic3—81no—
271C32×C8—21no—
272C3⋊(C3⋊C8)—21no—
273C3×C3⋊C8—21no—
274C3×C3⋊C8—21no—
275#540—91no—
276#520—91no—
277#481—91no—
278#480—91no—
279#479—91no—
280#478—91no—
281#460—31no—
282#459—91no—
283#449—31no—
284#449—91no—
285#442—91no—
286#440—91no—
287C4×SD16—91no—
288C4×D8—91no—
289#433—91no—
290C3×#41—62no—
291C3×#41—62no—
292C2×C3×Q8—21no—
293C2×C3×Q8C22×D311yescharacteristic
294C2×C3×Q8C22×D311yescharacteristic
295C2×C3×D4—21no—
296C2×C3×D4—31no—
297C2×C3×D4—31no—
298C2×C3×D4—61no—
299C2×C3×D4—61no—
300C2×C3×D4—61no—
301C2×C3×D4—61no—
302C2×C3×D4C22×D311yescharacteristic
303C2×C3×D4C22×D311yescharacteristic
304C22×C3×C4—31no—
305C22×C3×C4—61no—
306C2×#67—21no—
307C2×#67—21no—
308C2×#67—21no—
309C2×#67—61no—
310C2×#67—61no—
311C22×Dic3—61no—
312C22×Dic3—61no—
313C22×Dic3—61no—
314C22×Dic3—61no—
315C22×Dic3—61no—
316C22×Dic3—61no—
317C22×Dic3—121no—
318#239—22no—
319#239—22no—
320C2×D12—21no—
321C2×D12C22×D311yescharacteristic
322C2×D12C22×D311yescharacteristic
323C2×C4×D3—21no—
324C2×C4×D3—61no—
325C2×C4×D3—61no—
326C2×C4×D3—61no—
327C2×C4×D3—61no—
328C2×C4×D3C22×D311yescharacteristic
329C3×SD16—24no—
330C3×SD16—22no—
331C3×SD16—22no—
332C3×SD16—62no—
333C3×D8—62no—
334C2×C3×C8—21no—
335C2×C3×C8—31no—
336C2×C3×C8—31no—
337C2×C3×C8C22×D311yescharacteristic
338C2×C3×C8C22×D311yescharacteristic
339C3×C4⋊C4—31no—
340C3×C4⋊C4—31no—
341C3×C4⋊C4—61no—
342C3×C22⋊C4—61no—
343C3×C42—31no—
344C3×C42—61no—
345#217—21no—
346#217—31no—
347#217—31no—
348#217—61no—
349#217—61no—
350#217—61no—
351#217—61no—
352#217—61no—
353#217—61no—
354#217—121no—
355#215—22no—
356#213—22no—
357#213—62no—
358#213—62no—
359(C2×D3)⋊C4—31no—
360(C2×D3)⋊C4—31no—
361(C2×D3)⋊C4—61no—
362(C2×D3)⋊C4—61no—
363(C2×D3)⋊C4—61no—
364(C2×D3)⋊C4—61no—
365C4⋊Dic3—21no—
366C4⋊Dic3—31no—
367C4⋊Dic3—31no—
368C4⋊Dic3—31no—
369C4⋊Dic3—31no—
370C4⋊Dic3—31no—
371C4⋊Dic3—31no—
372C4⋊Dic3—61no—
373C4⋊Dic3—61no—
374C4⋊Dic3—61no—
375C4⋊Dic3—61no—
376C4⋊Dic3—61no—
377C4⋊Dic3—61no—
378C4⋊Dic3—121no—
379C4⋊Dic3C22×D311yescharacteristic
380C4⋊Dic3C22×D311yescharacteristic
381Dic3⋊C4—31no—
382Dic3⋊C4—31no—
383Dic3⋊C4—61no—
384Dic3⋊C4—61no—
385Dic3⋊C4—61no—
386Dic3⋊C4—61no—
387C4×Dic3—21no—
388C4×Dic3—31no—
389C4×Dic3—31no—
390C4×Dic3—61no—
391C4×Dic3—61no—
392C4×Dic3—61no—
393C4×Dic3—121no—
394C4×Dic3C22×D311yescharacteristic
395C2×C3⋊C8—31no—
396C2×C3⋊C8—31no—
397C2×C3⋊C8—61no—
398C2×C3⋊C8C22×D311yescharacteristic
399C2×C3⋊C8C22×D311yescharacteristic
400C22×C32—41no—
401C22×C32—41no—
402C22×C32—41no—
403C22×C32C22×D411yescharacteristic
404C2×C3×D3—21no—
405C2×C3×D3—22no—
406C2×C3×D3—21no—
407C2×C3×D3—21no—
408C2×C3×D3—41no—
409C2×C3×D3—41no—
410C2×C3×D3—41no—
411C2×C3×D3—41no—
412C2×C3×D3—41no—
413C32×C4—22no—
414C32×C4C2×#4111yescharacteristic
415C32×C4C2×#4111yescharacteristic
416C3⋊Dic3—21no—
417C3⋊Dic3—21no—
418C3⋊Dic3—41no—
419C3⋊Dic3—41no—
420C3×Dic3—21no—
421C3×Dic3—21no—
422C3×Dic3—21no—
423C3×Dic3—41no—
424C3×Dic3—41no—
425C2×#41—31no—
426C2×SD16—31no—
427C2×SD16D3211yescharacteristic
428C2×D8—31no—
429C2×D8—91no—
430#127—31no—
431#125—91no—
432#123—181no—
433#123—181no—
434#121—31no—
435#121—91no—
436#121—181no—
437#121—181no—
438C4×Q8—31no—
439C4×Q8—91no—
440C4×D4—91no—
441C4×D4—91no—
442C4×D4—91no—
443C4×D4—91no—
444C4×D4—181no—
445C4×D4—181no—
446#117—91no—
447#117—181no—
448C2×C4⋊C4—91no—
449C2×C4⋊C4—181no—
450#107—91no—
451#107—91no—
452#106—91no—
453#106—91no—
454C4⋊C8—31no—
455C4⋊C8—91no—
456#103—31no—
457#103—91no—
458#102—31no—
459#102—31no—
460#102—31no—
461#102—91no—
462#102—91no—
463#102—91no—
464C22⋊C8—31no—
465C22⋊C8—91no—
466#97—91no—
467C4×C8—91no—
468C23×C3—21no—
469C23×C3—21no—
470C23×C3—31no—
471C23×C3—41no—
472C23×C3—61no—
473C23×C3—61no—
474C22×D3—21no—
475C22×D3—21no—
476C22×D3D3×D411yescharacteristic
477C3×Q8—21no—
478C3×Q8—21no—
479C3×Q8—22no—
480C3×Q8—41no—
481C3×Q8#23712yes—
482C3×Q8#23712yes—
483C3×D4—22no—
484C3×D4—21no—
485C3×D4—21no—
486C3×D4—21no—
487C3×D4—21no—
488C3×D4—32no—
489C3×D4—41no—
490C3×D4—64no—
491C3×D4—61no—
492C3×D4—61no—
493C3×D4—61no—
494C3×D4—241no—
495C3×D4—241no—
496C3×D4—241no—
497C2×C3×C4—21no—
498C2×C3×C4—21no—
499C2×C3×C4—21no—
500C2×C3×C4—31no—
501C2×C3×C4—31no—
502C2×C3×C4—31no—
503C2×C3×C4—41no—
504C2×C3×C4—64no—
505C2×C3×C4—61no—
506C2×C3×C4—61no—
507C2×C3×C4—61no—
508C2×C3×C4—61no—
509C2×C3×C4C23×D311yescharacteristic
510C2×C3×C4C23×D311yescharacteristic
511#67—81no—
512#67—81no—
513#67—81no—
514#67—241no—
515#67—241no—
516C2×Dic3—21no—
517C2×Dic3—21no—
518C2×Dic3—31no—
519C2×Dic3—31no—
520C2×Dic3—31no—
521C2×Dic3—31no—
522C2×Dic3—61no—
523C2×Dic3—61no—
524C2×Dic3—61no—
525C2×Dic3—61no—
526C2×Dic3—61no—
527C2×Dic3—61no—
528C2×Dic3—121no—
529C2×Dic3—121no—
530C2×Dic3—241no—
531C2×Dic3—241no—
532C2×Dic3—241no—
533C2×Dic3—241no—
534C2×Dic3—241no—
535C2×Dic3—241no—
536C2×Dic3—242no—
537C2×Dic3D3×D411yescharacteristic
538C2×Dic3D3×D411yescharacteristic
539C2×Dic3D3×D411yescharacteristic
540D12—24no—
541D12—21no—
542D12—21no—
543D12—21no—
544D12#23712yes—
545C4×D3—24no—
546C4×D3—21no—
547C4×D3—21no—
548C4×D3—241no—
549C4×D3—241no—
550C4×D3—241no—
551C4×D3—241no—
552C3×C8—22no—
553C3×C8—21no—
554C3×C8—21no—
555C3×C8—61no—
556C3×C8—61no—
557C3⋊C8—21no—
558C3⋊C8—21no—
559C3⋊C8—61no—
560C3⋊C8—61no—
561C3⋊C8—121no—
562C2×C32—81no—
563C2×C32#52511yescharacteristic
564C2×C32#57611yescharacteristic
565C2×C32#57711yescharacteristic
566C3×D3—41no—
567C3×D3—42no—
568C3×D3—81no—
569#41—62no—
570#41—62no—
571C2×Q8C2×D3211yescharacteristic
572C2×D4—31no—
573C2×D4—31no—
574C2×D4—61no—
575C2×D4—61no—
576C2×D4—61no—
577C2×D4—61no—
578C2×D4—181no—
579C2×D4C2×D3211yescharacteristic
580C22×C4—31no—
581C22×C4—61no—
582C22×C4—181no—
583C22×C4—181no—
584C22×C4—181no—
585C22×C4—181no—
586C22×C4—181no—
587SD16—22no—
588SD16—62no—
589D8—62no—
590D8—182no—
591C2×C8—31no—
592C2×C8—31no—
593C2×C8—91no—
594C2×C8C2×D3211yescharacteristic
595C4⋊C4—31no—
596C4⋊C4—31no—
597C4⋊C4—61no—
598C4⋊C4—91no—
599C4⋊C4—91no—
600C4⋊C4—91no—
601C4⋊C4—91no—
602C4⋊C4—181no—
603C4⋊C4—181no—
604C4⋊C4—181no—
605C4⋊C4—181no—
606C22⋊C4—61no—
607C22⋊C4—91no—
608C22⋊C4—91no—
609C22⋊C4—181no—
610C22⋊C4—181no—
611C22⋊C4—181no—
612C22⋊C4—181no—
613C22⋊C4—181no—
614C42—31no—
615C42—61no—
616C42—91no—
617C42—181no—
618C22×C3—21no—
619C22×C3—42no—
620C22×C3—41no—
621C22×C3—41no—
622C22×C3—41no—
623C22×C3—41no—
624C22×C3—41no—
625C22×C3—41no—
626C22×C3—61no—
627C22×C3—61no—
628C22×C3—62no—
629C22×C3—61no—
630C22×C3—81no—
631C22×C3—81no—
632C22×C3—121no—
633C22×C3—121no—
634C22×C3—121no—
635C22×C3—121no—
636C22×C3—121no—
637C22×C3C2×D3×D411yescharacteristic
638C22×C3C2×D3×D411yescharacteristic
639C2×D3—21no—
640C2×D3—21no—
641C2×D3—21no—
642C2×D3—22no—
643C2×D3—41no—
644C2×D3—41no—
645C2×D3—41no—
646C2×D3—41no—
647C2×D3—41no—
648C3×C4—22no—
649C3×C4—22no—
650C3×C4—21no—
651C3×C4—21no—
652C3×C4—42no—
653C3×C4—61no—
654C3×C4—61no—
655C3×C4—61no—
656C3×C4—121no—
657C3×C4—121no—
658C3×C4C2×#23711yescharacteristic
659C3×C4C2×#23711yescharacteristic
660C3×C4C2×#23711yescharacteristic
661C3×C4D3×#4111yescharacteristic
662Dic3—21no—
663Dic3—21no—
664Dic3—21no—
665Dic3—41no—
666Dic3—41no—
667Dic3—61no—
668Dic3—61no—
669Dic3—61no—
670Dic3—61no—
671Dic3—121no—
672Dic3—121no—
673Dic3—121no—
674Dic3—121no—
675Dic3—121no—
676Dic3—121no—
677Dic3—241no—
678Dic3—241no—
679C32#311911yescharacteristic, complemented, Sylow
680C23—21no—
681C23—31no—
682C23—61no—
683C23—61no—
684Q8—21no—
685Q8#380512yes—
686D4—21no—
687D4—21no—
688D4—32no—
689D4—64no—
690D4—61no—
691D4—61no—
692D4—61no—
693D4—241no—
694D4—241no—
695D4—241no—
696D4—721no—
697C2×C4—21no—
698C2×C4—31no—
699C2×C4—31no—
700C2×C4—31no—
701C2×C4—64no—
702C2×C4—61no—
703C2×C4—61no—
704C2×C4—61no—
705C2×C4—61no—
706C2×C4—91no—
707C2×C4—91no—
708C2×C4—181no—
709C2×C4—181no—
710C2×C4—721no—
711C2×C4—721no—
712C2×C4—721no—
713C2×C4—721no—
714C2×C4—721no—
715C2×C4C22×D3211yescharacteristic
716C8—21no—
717C8—61no—
718C8—61no—
719C8—181no—
720C2×C3—21no—
721C2×C3—21no—
722C2×C3—21no—
723C2×C3—82no—
724C2×C3—81no—
725C2×C3—81no—
726C2×C3—121no—
727C2×C3—122no—
728C2×C3—241no—
729C2×C3#558611yescharacteristic
730C2×C3#560611yescharacteristic
731C2×C3#576211yescharacteristic
732C2×C3#576911yescharacteristic
733C2×C3#577411yescharacteristic
734C2×C3#577511yescharacteristic
735D3—41no—
736D3—42no—
737D3—81no—
738C22—41no—
739C22—41no—
740C22—41no—
741C22—62no—
742C22—61no—
743C22—61no—
744C22—61no—
745C22—121no—
746C22—121no—
747C22—121no—
748C22—121no—
749C22—121no—
750C22D32×D411yescharacteristic
751C4—22no—
752C4—61no—
753C4—61no—
754C4—61no—
755C4—121no—
756C4—121no—
757C4—181no—
758C4—181no—
759C4—361no—
760C4—361no—
761C4D3×#23711yescharacteristic
762C4C2×#380511yescharacteristic
763C3—21no—
764C3#8007211yescharacteristic, complemented
765C3#8036411yescharacteristic, complemented
766C2—81no—
767C2—121no—
768C2—122no—
769C2—241no—
770C2#1059474911yescharacteristic
771C2#1059475511yescharacteristic
772C2#1059513011yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×SD16C22
socleC22×C32C22×D4
hypercenterC2×SD16D32
hypocenterC32#3119
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×SD16

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. #10595394C2semidirect
2. #10595217C2semidirect
3. #10592863C2semidirect
4. C3×#5172C2semidirect
5. C3×#5163C2semidirect
6. #10591586C2semidirect
7. #10591571C2semidirect
8. #10591547C2semidirect
9. #10591435C2semidirect
10. #10591428C2semidirect
11. #10591415C2semidirect
12. #10590767C2semidirect
13. #10590741C2semidirect
14. #10590699C2semidirect
15. #10590680C2semidirect
69. #5172D3semidirect
73. #5163D3semidirect
679. C32#3119semidirect
764. C3#80072semidirect
765. C3#80364semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#105953942
#105952172
#105928632
C3×#51722
C3×#51632
#105915862
#105915712
#105915472
#105914352
#105914282
#105914152
#105907672
#105907412
#105906992
#105906802
#803643
#800723